Finite-Time Synchronization in a Novel Discrete Fractional SIR Model for COVID-19

This paper proposes a novel discrete fractional-order (FO) SIR model to capture the complex transmission dynamics of COVID-19. By incorporating memory effects via Caputo fractional difference operators, the model extends the classical SIR framework to account for nonlocal interactions and historical dependencies inherent in epidemic data. A master-slave configuration is introduced, and sufficient conditions for finite-time synchronization (FTSY) between these systems are derived using the Lyapunov stability theory and the discrete Mittag–Leffler function. The analysis demonstrates that, under appropriate control laws, the error dynamics between the master and slave systems converge to zero within a finite settling time. Numerical simulations are provided to validate the theoretical findings, illustrating the impact of various parameters on the evolution of susceptible, infected, and recovered populations. The integration of fractional calculus in this discrete framework enhances the accuracy of epidemic predictions and offers a robust control strategy for coordinating interventions across different regions.